Generalized magneto-thermoelasticity of a layer based on the Lord–Shulman and Green–Lindsay theories

Abstract

In this research, development and solution of the generalized magneto-thermoelastic response of a layer based on both Lord–Shulman and Green–Lindsay theories are reported. To this end, the Maxwell electromagnetism equations are reduced to one-dimensional space. The Lorentz force is applied to obtain the magnetic body force and extract the effect of the magnetic field effect on the equation of motion of the layer. The heat conduction equation is also established for the one-dimensional layer using both the Lord–Shulman and Green–Lindsay theories. The established equations are four in number in terms of displacement, temperature change, induced magnetic field and electric field. Equations are reformulated in a dimensionless presentation where the speed of waves is also changed. Using the generalized differential quadrature method, the established dimensionless equations are discreted and provided in a matrix representation. Next, using Newmark time marching scheme, equations are traced in time. At first results of this study are compared with the available data in the open literature. After that novel results are given for a layer. It is shown that under both of the mentioned theories, temperature propagates with finite speed where the speed of wave may be obtained using the relaxation times.